Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion 7) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.

Answer 1

Solution :

n = 300

x = 112

$\hat p$ = x / n = 112/ 300 = 0.373

1 -$\hat p$ = 1 - 0.373 = 0.627

At 98% confidence level the t is ,

$\alpha$ = 1 - 98% = 1 - 0.98 = 0.02

$\alpha$ / 2 = 0.02 / 2 = 0.01

Z_$\alpha$/2 = Z_0.01 = 2.326

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$(($\hat p$ * (1 - $\hat p$)) / n)

= 2.326 * ($\sqrt$((0.373 * 0.627) / 300)

= 0.065

A 90 % confidence interval for population proportion p is ,

$\hat p$ - E

0.373 - 0.065

308

The Republican candidate is 308